Bridging the Gap Problem-Solving. First Thoughts … Form 5A has 30 pupils: 10 Rovers fans 20 United...

Bridging the Gap

Problem-Solving

First Thoughts …Form 5A has 30 pupils:

10 Rovers fans

20 United fans

Form 5B has 18 pupils:

9 Rovers fans

9 United fansYou’re a Rovers fan. Which class would you rather be in?

Did You Pick 6A?

5A: 10 + 20 = 30 5B: 9 + 9 = 18

– Rani, a mad Rovers fan, picked 5A:

“10 is bigger than 9,

so there’s more Rovers fans in 5A than 5B.

Yey!”

Did You Pick 6B?

5A: 10 + 20 = 30 5B: 9 + 9 = 18

- But other red Rovers fans picked 5B:

MARTIN SAYS

“I’m not going to 5A - I’d be outnumbered 2

United to every 1 Rovers fan!”

BECKY SAYS:“Only one third of 5A

Rovers fans. It’s one half in

5B.

HANNAH SAYS:

“5A only has 10 out has 10 out of 30 Roversof 30 Rovers fans.

That’s 1 out of 3.”

2 to 1

is a ratiothird and half are fractions

1 out of 3 is a

proportion

All answers are correct! But - 3 different sorts of answer.

Recap – 3 Ways to Compare Numbers

Fraction?

Proportion?

Ratio?

Which question is a …“5A only has 10 out has 10 out

of 30 Roversof 30 Rovers fans. That’s 1 out of 3.”

“Only one third of 5A Rovers fans.

It’s one half in 5B.”

“I’m not going to 5A.

I’d be outnumbered 2 to every 1.”

What’s the Difference - Summing Up: .

“1 to every 2” is a Ratio“1 Rovers fan to every 2 United fans”“The ratio of Rovers to United fans is 1 to 2”“The ratio of United to Rovers fans is 2 to 1”

“1 out of 3” is a Proportion“1 out of every 3 fans is a Rovers fan”“The proportion of Rover fans is 1 out of 3”

“One third” is a Fraction“One third of all fans are Rovers fans“1/3 of all fans are Rovers fans”

Ratios compare PART

WITH PART

Proportions compare PART WITH WHOLE

Fractions compare PART WITH WHOLE

using shorthand such as 1/3

3 different ways to say the same thing

3 different ways to compare numbers

So comparing totals isn’t the only way to look at these numbers…

Form 5A has 30 pupils:

10 Rovers fans

20 United fans

Form 5B has 18 pupils:

9 Rovers fans

9 United fans

…You can compare part with part using RATIO

…You can compare part with whole using

PROPORTIONS or FRACTIONS

Eg: 1/3 are Rovers fansEg: 1 out of 3 are Rovers fans

Eg: Rovers : United = 1 to every 2 = 1:2

Ratio, Proportion or Fraction?two out of five

This is a … proportion

two fifths

This is a … fractionfour tenths

This is a … fractionfour to every ten

This is a … ratioten to every four

This is a … ratiofour out of ten

This is a … proportion4/10

This is a … fraction 4:10

This is a … ratio

Ratio, Proportion or Fraction?3 United fans to every 2 Rangers fans

This is a …ratio

9 girls out of 10 use soap

This is a …proportion

3 boys out of 10 use deodorant


Ratio, Proportion or Fraction?3 out of 4 pizza-munchers love olives


Half of all girls in 6D love History

This is a …fraction

One third of all road accidents involve drinking


Ratio, Proportion or Fraction?3 out of 4 drivers speed at some time


Three quarters of drivers speed


3 drivers speed to every 1 which does not

This is a …ratio

1 girl to every 2 boys

2 girls to every 4 boys



girls : boys = 4 : 8




But the simplest ratio is still 1 : 2



This is the simplest ratio is 1 : 2

The dinner queue

Ratio of girls to boys?

2 boys to every 1 girl

4 boys to every 2 girls



boys : girls = 8 : 4







This is the simplest ratio is 2 : 1

Ratio of boys to girls?

The dinner queue

1 girl out of 3

2 girls out of 6

3 girls out of 9

4 girls out of 12

Simplest proportion of girls is still 1 out of 3



This is the simplest proportion of girls =

1 out of 3

The dinner queue

What proportion is girls?

Proportion of boys?

Simplest proportion of boys?

Proportion of boys?


Proportion of boys?


Proportion of boys?

4 boys out of 6

6 boys out of 9

8 boys out of 12

Simplest proportion of boys is still 2 out of 3




This is the simplest proportion of boys

= 2 out of 3

2 boys out of 3

The dinner queue

What proportion is boys?

What fraction is girls?

Simplest proportion of girls?


Simplest fraction of girls?


Simplest fraction of girls?


2 / 6

3 / 9

4 / 12

Simplest fraction of girls is still 1 / 3



Simplest fraction of girls? This is the simplest

fraction of girls = 1 / 3

1 / 3

The dinner queue


What fraction is boys?



Simplest fraction of boys?



4 / 6

6 / 9

8 / 12

Simplest fraction of boys is still 2 / 3




This is the simplest fraction of boys = 2 / 3

The dinner queue


What fraction is boys?2 / 3

Bridging the Gap Problem-Solving. First Thoughts … Form 5A has 30 pupils: 10 Rovers fans 20 United...

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